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A229493
Irregular triangle in which row n has numbers k such that prime(n) divides A001008(k), the numerator of the k-th harmonic number.
1
2, 7, 22, 4, 20, 24, 6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728, 3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888, 958, 962, 966, 1291, 1293, 9328, 9331, 9335, 9338, 9376, 9378, 10583, 10587, 10591, 14205, 14207
OFFSET
2,1
COMMENTS
The length of each row is given in A092103.
LINKS
David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302. [WARNING: Table 2 contains miscalculations for p=19, 47, 59, ... - Max Alekseyev, Oct 23 2012]
A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.
C. Sanna, On the p-adic valuation of harmonic numbers, J. Number Theory 166 (2016), 41-46.
EXAMPLE
The irregular triangle begins:
2, 7, 22
4, 20, 24
6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728
3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888,...
MATHEMATICA
(* rows 2, 3, and part of 4 *) h = ParallelTable[Numerator[HarmonicNumber[i]], {i, 10000}]; Flatten[Table[Position[h, _?(Mod[#, p] == 0 &)], {p, {3, 5, 7}}]]
CROSSREFS
Cf. A092103 (number of k for which prime(n) divides A001008(k)).
Sequence in context: A150321 A076716 A088591 * A175871 A137107 A284921
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved